(-infinity, -2/3)u(-2/3,0)u(0, infinity)
since it is asking for f(g(x)) we plug g into x which looks like:
now we plug that into the f(x) equation for all of the x's because that is what replaced the x so:
we look at the denominator so we can pull the 2/x+3 out and set it equal to zero, therefore solving for x
this gives us -2/3
and we get the 0 from g(x) 's denominator
that should be correct and hope this helps!
The Domain is all real values of x except x = 0 and x = -2.5.
I am assuming that f(x) = 3/(x + 2).
(f o g)x is found by substituting 5/x for the x in 3/(x + 2).
(f o g) x = 3/ ( 5/x + 2)
= 3 / ( 5+2x) / x
= 3x / (5 + 2x).
When finding the domain you first check for values of x which make g(x) undefined then values of x which make (f o g)(x) undefined.
x = 0 makes g(x) = 5/0 so it is undefined and x = -2.5 makes g o f undefined also.